关于Hermite与次Hermite二次矩阵方程解的研究

On the Solutions of Quadratic Matrix Equation of Hermite and Sub-Hermite Matrix

以Hermite矩阵、斜Hermite矩阵与次Hermite矩阵、次斜Hermite矩阵的相近关系为基础，证明了从Hermite二次矩阵方程的矩阵解出发，可得到次Hermite二次矩阵方程的解的相应结果．应用这种方法，不仅给出了可概括这两类矩阵方程解的已有结论的充要条件，而且指出已有文献得到的是不以-1为特征值的矩阵解，因此，这些矩阵方程的“一般解”的研究还没有结束．

Based on the connection relationships among Hermite matrix, skew-Hermite matrix and sub-Hermite matrix,sub-skew-Hermite matrix, the corresponding conclusions of quadratic sub-hermite matrix equations have been obtained by the matrix solution of quadratic Hermite matrix equations. Used method like this, not only the necessary and sufficient conditions which can summary the present conclusions of solutions to these two classes matrix equations are given, but also the matrix solution of present literatures are pointed out that their eigenvalues are not -1. Therefore, the general solutions to these matrix equations are not the end.